The first homotopic Baire class of maps with values in ANR's coincides with the first Baire class

TL;DR

This paper introduces a homotopical version of the first Baire class of maps and proves that, when valued in ANR spaces, it coincides with the classical first Baire class, linking homotopy theory with descriptive set theory.

Contribution

It defines the first homotopic Baire class of maps and establishes its equivalence with the classical first Baire class for maps into ANR spaces.

Findings

Homotopic Baire class coincides with the classical Baire class for ANR-valued maps.

Establishes a homotopical framework for Baire class analysis.

Bridges concepts between homotopy theory and descriptive set theory.

Abstract

We introduce the first homotopic Baire class of maps as a homotopical counterpart of a usual first Baire class of maps between topological spaces and show that those classes with values in ANR spaces coincide